Question: Rewrite the following equation in logarithmic form. 100 = 10 2 100=10\^{ {2}} Rewrite the following equation in exponential form. $ \log_{5}{\left(\dfrac{1}{125}\right)}=-3 $
The inverse relationship of exponents and logarithms For $m>0$ and $b>0, b\neq 1$, we have the following relationship: b q = m { b\^{{ q}}}}= m if and only if $ \log_{ b }{ m}=D q$ Converting the exponential equation So 10 2 = 100 \, {{10}\^{ {2}}}}= {100}\, implies that $\,\log_{ {10}}({ {100}})=D {2}$. This can also be written as $\log(100)=2$ [What happened to the base?] Converting the logarithmic equation Similarly $\, \log_{ 5}\left({{\dfrac{1}{125}}}\right)=-3}\,$ implies that 5 − 3 = 1 125 \, 5\^{D { {-3}}}={\dfrac{1}{125}}. The logarithmic form of 100 = 10 2 100=10\^{{2}} is: $\,\log{{(100)}}={2}$ The exponential form of $ \log_{5}{\left(\dfrac{1}{125}\right)}=-3$ is: 5 − 3 = 1 125 \,5\^{{ {-3}}}={\dfrac{1}{125}}